arXiv:2607.06026cs.LGcs.NA2026-07

用样条网络直接在CAD模型上做壳结构分析,无需数据转换。

SplineNet: An Isogeometric Deep Learning Method for Complex Shells

论文配图:SplineNet: An Isogeometric Deep Learning Method for Complex Shells
图 1 · 摘自论文原文
  • 基于无缺陷样条表示构建神经网络,实现精确几何描述。
  • 可零数据或有数据训练,能量项直接作为损失函数提升精度。
  • 适合需要高精度建模的复杂结构设计与工程仿真场景。

我们提出一种新型等几何深度学习方法——SplineNet,用于复杂壳结构的无缝设计与分析。该方法基于水密样条表示(如分析适用的非结构化T样条),在神经网络中实现计算机辅助设计(CAD)模型的精确几何描述。通过贝齐尔提取构建网络架构,伯恩斯坦多项式作为非线性激活函数。SplineNet支持零数据或数据驱动模式:在零数据情况下,能量形式可自然作为损失项,满足计算机辅助工程(CAE)需求且可精确计算;特别地,采用基尔霍夫-洛夫(KL)模型求解壳结构力学行为。由此,CAD与CAE可在神经网络中紧密集成,避免耗时的模型/数据交换。在数据驱动模式下,SplineNet可作为深度算子网络(DeepONet)的主干网络,提供可解释性。给定训练好的网络和未见输入数据,可即时获得结果,无需重新训练或重复传统分析流程。最后,多种数值算例验证了该方法在真实复杂几何下的有效性。

原文摘要 · Abstract (English)

We present a novel isogeometric deep learning method, termed SplineNet, for the seamless design and analysis of shell structures with complex geometries. The proposed approach is built upon watertight spline representations, e.g., analysis-suitable unstructured T-splines, and features exact geometric descriptions of Computer-Aided Design (CAD) models in neural networks. Bézier extraction is used to build the network architecture, where Bernstein polynomials serve as the nonlinear activation functions. SplineNet can be applied in a data-free or data-driven way. In the data-free case, energy-based formulations can be naturally incorporated as loss terms, which fulfill the need of Computer-Aided Engineering (CAE) and can be accurately calculated. In particular, the Kirchhoff--Love (KL) model is adopted to solve for the mechanical behaviors of shell structures. This way, CAD and CAE can be tightly integrated in a deep neural network without the time-consuming model/data exchange process. In the data-driven case, SplineNet can be used as the trunk net of Deep Operator Networks (DeepONet) to provide interpretability. Given such a trained network and unseen input data, results can be immediately obtained without retraining the network or repeatedly performing the traditional workflow for analysis. In the end, a variety of numerical examples are studied to demonstrate the effectiveness of the proposed method, especially when real-world complex geometries are involved.

等几何分析深度学习壳结构

Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品;中文卡片由大模型生成,请以原文为准。